# Automatic Differentiation in EagerPy

EagerPy uses a functional approach to automatic differentiation. You first define a function that will then be differentiated with respect to its inputs. This function is then passed to ep.value_and_grad to evaluate both the function and its gradient. More generally, you can also use ep.value_aux_and_grad if your function has additional auxiliary outputs and ep.value_and_grad_fn if you want the gradient function without immediately evaluating it at some point x.

Using ep.value_and_grad for automatic differentiation in EagerPy:

import torch
x = torch.tensor([1., 2., 3.])

# The following code works for any framework, not just Pytorch!

import eagerpy as ep
x = ep.astensor(x)

def loss_fn(x):
    # this function takes and returns an EagerPy tensor
    return x.square().sum()

# PyTorchTensor(tensor(14.))

print(ep.value_and_grad(loss_fn, x))
# (PyTorchTensor(tensor(14.)), PyTorchTensor(tensor([2., 4., 6.])))